The equation of stationary wave is

$\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)$

Which of the following is NOT correct

  • [JEE MAIN 2024]
  • A

    The dimensions of nt is $[L]$

  • B

    The dimensions of $n$ is $\left[\mathrm{LT}^{-1}\right]$

  • C

    The dimensions of $n / \lambda$ is $[T]$

  • D

    The dimensions of $x$ is $[L]$

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  • [KVPY 2020]

A force defined by $F=\alpha t^2+\beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:

  • [NEET 2024]

Choose the correct match

List I 

List II

 $(i)$ Curie

 $(A)$ $ML{T^{ - 2}}$

 $(ii)$ Light year 

 $(B)$ $M$

 $(iii)$ Dielectric strength

 $(C)$ Dimensionless

 $(iv)$ Atomic weight

 $(D)$ $T$

 $(v)$ Decibel

 $(E)$ $M{L^2}{T^{ - 2}}$

 

 $(F)$ $M{T^{ - 3}}$

 

 $(G)$ ${T^{ - 1}}$

 

 $(H)$ $L$

 

 $(I)$ $ML{T^{ - 3}}{I^{ - 1}}$

 

 $(J)$ $L{T^{ - 1}}$

  • [IIT 1992]

Even if a physical quantity depends upon three quantities, out of which two are dimensionally same, then the formula cannot be derived by the method of dimensions. This statement